Notice that our smoothness condition in Definition REF  is slightly stronger than the standard Hölder smoothness condition in the nonparametric literature [1]}. In particular, we require that \(f^{(\ell )}(x|y,)\)  is Hölder continuous with some exponent \(0 < \zeta \le 1\)  in (REF ). This additional assumption is essential to show the rate of the bias estimator \(\hat{\mu }\)  in (REF ).
